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Information
| Code | ISB008 |
| Name | Monte Carlo Statistical Methods |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to give students how to do the statistical computing based on the approximating tools of Monte Carlo.
Course Content
Random number generation Monte Carlo İntegral, Bootstrap, Monte Carlo optimization, EM algorithm, Metropolis-Hastings algorithm, Gibbs sampler, Density estimation, Nonparametric regression
Course Precondition
None
Resources
Introducing Monte Carlo Methods with R, Christian Robert, George Casella, Springer, 2010.
Notes
Statistical Computing with R, Maria L. Rizzo, First Edition (Chapman and Hall/CRC The R Series), 2007.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Generates random numbers from a given distribution. |
| LO02 | Computes integrals approximately by using Monte Carlo methods. |
| LO03 | Controls and accelerates the convergence of the algorithms. |
| LO04 | Uses Monte Carlo methods in optimization. |
| LO05 | Uses Monte Carlo methods in Bayesian statistical analysis. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Develops new methods and strategies in modeling statistical problems and generating problem-specific solutions. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Can do detailed research on a specific subject in the field of statistics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Have a good command of statistical theory to contribute to the statistical literature. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Can use the knowledge gained in the field of statistics in interdisciplinary studies. | 4 |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Can organize projects and events in the field of statistics. | |
| PLO06 | Yetkinlikler - Öğrenme Yetkinliği | Can perform the stages of creating a project, executing it and reporting the results. | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Have the ability of scientific analysis. | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Can produce scientific publications in the field of statistics. | 2 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Have analytical thinking skills. | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Can follow professional innovations and developments both at national and international level. | |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Can follow statistical literature. | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | Can improve his/her foreign language knowledge at the level of making publications and presentations in a foreign language. | |
| PLO13 | Bilgi - Kuramsal, Olgusal | Can use information technologies at an advanced level. | |
| PLO14 | Bilgi - Kuramsal, Olgusal | Have the ability to work individually and make independent decisions. | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have the qualities necessary for teamwork. | |
| PLO16 | Bilgi - Kuramsal, Olgusal | Have a sense of professional and ethical responsibility. | 4 |
| PLO17 | Bilgi - Kuramsal, Olgusal | Acts in accordance with scientific ethical rules. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to R program | Source reading | |
| 2 | Random number generation | Source reading | |
| 3 | Controlling the acceleration of the algorithms | Source reading | |
| 4 | Controlling the acceleration of the algorithms II | Source reading | |
| 5 | Monte Carlo integration | Source reading | |
| 6 | Maximum likelihood method | Source reading | |
| 7 | Maximizing the likelihood and Monte Carlo approach for other optimization problems | Source reading | |
| 8 | Mid-term exam | Reviewing the topics | |
| 9 | EM algorithm for mixture models | Source reading | |
| 10 | Gibbs sampler | Source reading | |
| 11 | Bayesian estimators | Source reading | |
| 12 | Metropolis Hastings algorithm | Source reading | |
| 13 | Density estimation | Source reading | |
| 14 | Nonparametric regression | Source reading | |
| 15 | Nonparametric regression II | Source reading | |
| 16 | Final exam | Reviewing the topics | |
| 17 | Final exam | Reviewing the topics |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||